thoughts about learning…and other matters

Why do we have to learn proofs?

Yes, some students enjoy writing proofs. They accept the task as a challenging puzzle, one that provides an agreeable sense of completion once you’ve successfully threaded a path from the given information to the conclusion.

I was one of those students. But we were — and are — in the minority. The majority of students find proof-writing difficult, inscrutable, and not very interesting. Worse yet, they find it pointless. This may be especially true when the artificial strictures of two-column proofs are imposed.

One remedy for teachers and learners alike is to read two engaging essays: “What Is Mathematics For?” by Underwood Dudley, and “Why do we have to learn proofs!?” by Joshua N. Cooper. Both of these make it very clear that the current trend of justifying math by its practical, sometimes even career-oriented, real-life applications is misleading at best and dishonest at worst. The major reason to learn algebra, proofs, and other parts of mathematics is that they teach you to become a critical thinker. I admit that math isn’t always taught that way, but it should be. Treating a proof as a puzzle isn’t dumbing it down, it’s the essence of logical thinking.

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About me

I am starting my 21st year as a math teacher at Weston High School (the only public high school in Weston, MA, though sometimes it seems more like a private school). This is my 44th year as a teacher altogether. I also teach at Harvard’s Crimson Summer Academy each summer (this was the 15th!), and for 21 years I taught at the Saturday Course in Milton, MA. Until recently I served on the board of the Dorchester Historical Society.

I read, cook, and build my model railroad when I can. For some reason I’m left with less free time than would be ideal, but somehow I also manage to devote time to my wife, Barbara, and to our excessive number of cats.